Pub Date : 2026-06-15Epub Date: 2026-02-18DOI: 10.1016/j.fss.2026.109821
Hao Ying , Sanyang Liu , Kaibo Shi , Shouming Zhong , Kun Zhou
This paper investigates the stability and stabilization problems for T-S fuzzy systems with two stochastic additive time-varying delays. By taking full account of the stochastic characteristics of these delays, the original system is equivalently reformulated into a new system representation. In contrast to existing works, a controller accounting for two stochastic additive delays is designed using a delay partitioning approach. Subsequently, a structurally simple Lyapunov-Krasovskii functional (LKF) is constructed to effectively utilize the information regarding two stochastic time-varying delays and their derivatives. Based on this LKF, novel delay-derivative/distribution-dependent stability and stabilization criteria are derived, which are less conservative compared to previous results. Finally, the advantages and effectiveness of the proposed methods are demonstrated through three widely used numerical examples and a practical truck-trailer system.
{"title":"Delay-derivative/distribution dependent stability and stabilization criteria for T-S fuzzy systems with two additive stochastic time-varying delays","authors":"Hao Ying , Sanyang Liu , Kaibo Shi , Shouming Zhong , Kun Zhou","doi":"10.1016/j.fss.2026.109821","DOIUrl":"10.1016/j.fss.2026.109821","url":null,"abstract":"<div><div>This paper investigates the stability and stabilization problems for T-S fuzzy systems with two stochastic additive time-varying delays. By taking full account of the stochastic characteristics of these delays, the original system is equivalently reformulated into a new system representation. In contrast to existing works, a controller accounting for two stochastic additive delays is designed using a delay partitioning approach. Subsequently, a structurally simple Lyapunov-Krasovskii functional (LKF) is constructed to effectively utilize the information regarding two stochastic time-varying delays and their derivatives. Based on this LKF, novel delay-derivative/distribution-dependent stability and stabilization criteria are derived, which are less conservative compared to previous results. Finally, the advantages and effectiveness of the proposed methods are demonstrated through three widely used numerical examples and a practical truck-trailer system.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109821"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-15Epub Date: 2026-02-20DOI: 10.1016/j.fss.2026.109837
C. Mariya , Sunil Mathew , J.N. Mordeson
This article examines the structural properties of transitive fuzzy graphs, an important subclass of fuzzy graphs. We perform a detailed edge analysis and establish explicit relationships between different edge types and their membership degrees. Using path length, we develop a characterization of transitive fuzzy graphs. We further introduce and analyze specific subgraphs showing that the minimal connected spanning transitive subgraph that preserves the original graph’s connectivity strength is its maximum spanning tree. Finally, we propose an algorithm for constructing optimal transitive fuzzy blocks with the maximum number of fuzzy bridges.
{"title":"Transitive fuzzy graphs: Modeling, properties, and applications in network QoS enhancement","authors":"C. Mariya , Sunil Mathew , J.N. Mordeson","doi":"10.1016/j.fss.2026.109837","DOIUrl":"10.1016/j.fss.2026.109837","url":null,"abstract":"<div><div>This article examines the structural properties of transitive fuzzy graphs, an important subclass of fuzzy graphs. We perform a detailed edge analysis and establish explicit relationships between different edge types and their membership degrees. Using path length, we develop a characterization of transitive fuzzy graphs. We further introduce and analyze specific subgraphs showing that the minimal connected spanning transitive subgraph that preserves the original graph’s connectivity strength is its maximum spanning tree. Finally, we propose an algorithm for constructing optimal transitive fuzzy blocks with the maximum number of fuzzy bridges.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109837"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-15Epub Date: 2026-02-18DOI: 10.1016/j.fss.2026.109822
Yonghong Shen , Qian Wang
Based on the well-behaved algebraic structure and topological properties of the space of asymmetric linearly correlated fuzzy numbers, this paper presents a unified methodology for addressing the construction of the general solution and the stability analysis of the equilibrium solution of two-dimensional (2D) linear fuzzy differential systems. Specifically, leveraging the structural advantages of , a 2D linear fuzzy differential system with a crisp coefficient matrix can be equivalently transformed into two mutually independent classical linear differential systems that share the same coefficient matrix. Thereafter, the stability of the equilibrium solution is determined and the general solution is constructed by utilizing the mature stability theory and solution methods for planar linear systems. For a 2D linear fuzzy differential system with a fuzzy coefficient matrix, by virtue of the structural features of and the favorable properties of the distributive product (which unifies the A-cross product and complex product), the system can be equivalently converted into a coupled fourth-order real-valued linear differential system. The stability analysis of the equilibrium solution and the construction of the general solution are then implemented using the theory of real-valued linear differential systems. Meanwhile, a detailed procedure is proposed to clearly and efficiently guide the stability analysis and solution process of such linear fuzzy differential systems. Several illustrative examples are provided to verify the feasibility and effectiveness of the proposed methods, particularly by specializing the distributive product to the A-cross product and complex product, respectively. Finally, as an application, the temporal evolution behaviors of charge and current in an LC oscillatory circuit under different fuzzy disturbance environments (including fuzzy initial conditions, fuzzy inductance, and fuzzy capacitance) are analyzed, which demonstrates the practical applicability of the proposed theoretical framework.
{"title":"General solutions and stability analysis of two-dimensional linear fuzzy differential systems in the space of asymmetric linearly correlated fuzzy numbers","authors":"Yonghong Shen , Qian Wang","doi":"10.1016/j.fss.2026.109822","DOIUrl":"10.1016/j.fss.2026.109822","url":null,"abstract":"<div><div>Based on the well-behaved algebraic structure and topological properties of the space <span><math><msub><mi>R</mi><mrow><mi>F</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msub></math></span> of asymmetric linearly correlated fuzzy numbers, this paper presents a unified methodology for addressing the construction of the general solution and the stability analysis of the equilibrium solution of two-dimensional (2D) linear fuzzy differential systems. Specifically, leveraging the structural advantages of <span><math><msub><mi>R</mi><mrow><mi>F</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msub></math></span>, a 2D linear fuzzy differential system with a crisp coefficient matrix can be equivalently transformed into two mutually independent classical linear differential systems that share the same coefficient matrix. Thereafter, the stability of the equilibrium solution is determined and the general solution is constructed by utilizing the mature stability theory and solution methods for planar linear systems. For a 2D linear fuzzy differential system with a fuzzy coefficient matrix, by virtue of the structural features of <span><math><msub><mi>R</mi><mrow><mi>F</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msub></math></span> and the favorable properties of the distributive product (which unifies the <em>A</em>-cross product and complex product), the system can be equivalently converted into a coupled fourth-order real-valued linear differential system. The stability analysis of the equilibrium solution and the construction of the general solution are then implemented using the theory of real-valued linear differential systems. Meanwhile, a detailed procedure is proposed to clearly and efficiently guide the stability analysis and solution process of such linear fuzzy differential systems. Several illustrative examples are provided to verify the feasibility and effectiveness of the proposed methods, particularly by specializing the distributive product to the <em>A</em>-cross product and complex product, respectively. Finally, as an application, the temporal evolution behaviors of charge and current in an LC oscillatory circuit under different fuzzy disturbance environments (including fuzzy initial conditions, fuzzy inductance, and fuzzy capacitance) are analyzed, which demonstrates the practical applicability of the proposed theoretical framework.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109822"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-15Epub Date: 2026-02-11DOI: 10.1016/j.fss.2026.109817
Weiwei Tu
In this article, the issue of robust sliding mode fault-tolerant control is investigated for Takagi-Sugeno (T-S) fuzzy systems in the presence of actuator failures and disturbances. With a modified barrier function as well as a membership function-dependent sliding variable exploited, a novel sliding mode control scheme is developed such that a fuzzy reduced-order sliding mode is established without reaching phase. In comparison with the state-of-the-art results, the findings features series of merits. First, the sliding mode controller is proposed via the property of a class of modified barrier functions, the responses of fuzzy systems are within a preset sliding band, in which the sliding mode cannot be lost even though in the occurrence of faulty modes. Second, more designs of degree are provided via the proposal for calibrating the upper boundaries of system trajectories. Third, upon a membership function-dependent sliding variable, a reduced-order sliding mode with parallel distribution compensation (PDC) control framework is derived, which are with less conservativeness results than the classic ones of reduced-order sliding mode. Finally, some examples for simulation are offered to confirm the theoretical schemes.
{"title":"Membership function-dependent robust sliding mode fault-tolerant control for T-S fuzzy systems with disturbances: A preset sliding band scheme","authors":"Weiwei Tu","doi":"10.1016/j.fss.2026.109817","DOIUrl":"10.1016/j.fss.2026.109817","url":null,"abstract":"<div><div>In this article, the issue of robust sliding mode fault-tolerant control is investigated for Takagi-Sugeno (T-S) fuzzy systems in the presence of actuator failures and disturbances. With a modified barrier function as well as a membership function-dependent sliding variable exploited, a novel sliding mode control scheme is developed such that a fuzzy reduced-order sliding mode is established without reaching phase. In comparison with the state-of-the-art results, the findings features series of merits. First, the sliding mode controller is proposed via the property of a class of modified barrier functions, the responses of fuzzy systems are within a preset sliding band, in which the sliding mode cannot be lost even though in the occurrence of faulty modes. Second, more designs of degree are provided via the proposal for calibrating the upper boundaries of system trajectories. Third, upon a membership function-dependent sliding variable, a reduced-order sliding mode with parallel distribution compensation (PDC) control framework is derived, which are with less conservativeness results than the classic ones of reduced-order sliding mode. Finally, some examples for simulation are offered to confirm the theoretical schemes.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109817"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-15Epub Date: 2026-02-08DOI: 10.1016/j.fss.2026.109818
Piotr Nowak, Olgierd Hryniewicz
Fuzzy random variables were introduced to model uncertain quantities being simultaneously random and imprecise. Convergence of sequences and series of random variables is an important issue within theoretical considerations and practical applications. For fuzzy random variables, several types of convergence have been defined. In this paper, we focus on the almost sure convergence, the convergence in probability, and the convergence in distribution of series of independent fuzzy random variables taking values in the space of the fuzzy subsets of with nonvoid convex compact α-cuts and support functions being integrable of order p for a fixed positive integer d and p ≥ 1. For these series, we formulate and prove a counterpart of the Itô–Nisio Theorem, characterizing convergence in a separable Banach space. In the case of , we also obtain a fuzzy counterpart of the Three Series Theorem. Finally, we prove some theorems concerning the convergence in the q-th mean as well as the q-th and the exponential moments of series of independent -valued random variables for q > 0.
{"title":"On convergence of series of independent fuzzy random variables","authors":"Piotr Nowak, Olgierd Hryniewicz","doi":"10.1016/j.fss.2026.109818","DOIUrl":"10.1016/j.fss.2026.109818","url":null,"abstract":"<div><div>Fuzzy random variables were introduced to model uncertain quantities being simultaneously random and imprecise. Convergence of sequences and series of random variables is an important issue within theoretical considerations and practical applications. For fuzzy random variables, several types of convergence have been defined. In this paper, we focus on the almost sure convergence, the convergence in probability, and the convergence in distribution of series of independent fuzzy random variables taking values in the space <span><math><mrow><msubsup><mi>F</mi><mrow><mi>c</mi><mi>o</mi><mi>c</mi><mi>p</mi></mrow><mrow><mi>n</mi><mi>o</mi></mrow></msubsup><mrow><mo>(</mo><msup><mi>R</mi><mi>d</mi></msup><mo>)</mo></mrow></mrow></math></span> of the fuzzy subsets of <span><math><msup><mi>R</mi><mi>d</mi></msup></math></span> with nonvoid convex compact <em>α</em>-cuts and support functions being integrable of order <em>p</em> for a fixed positive integer <em>d</em> and <em>p</em> ≥ 1. For these series, we formulate and prove a counterpart of the Itô–Nisio Theorem, characterizing convergence in a separable Banach space. In the case of <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span>, we also obtain a fuzzy counterpart of the Three Series Theorem. Finally, we prove some theorems concerning the convergence in the <em>q</em>-th mean as well as the <em>q</em>-th and the exponential moments of series of independent <span><math><mrow><msubsup><mi>F</mi><mrow><mi>c</mi><mi>o</mi><mi>c</mi><mi>p</mi></mrow><mrow><mi>n</mi><mi>o</mi></mrow></msubsup><mrow><mo>(</mo><msup><mi>R</mi><mi>d</mi></msup><mo>)</mo></mrow></mrow></math></span>-valued random variables for <em>q</em> > 0.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109818"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146175572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-15Epub Date: 2026-02-17DOI: 10.1016/j.fss.2026.109832
Juscelino Araújo , Benjamín Bedregal , Ana Shirley Monteiro , Regivan Santiago , Eduardo Palmeira
This paper studies e-operators. They are a class of mappings that allow the extension of operations defined on a lattice to a larger one while preserving key algebraic properties. A characterization of these mappings is presented. It is shown that operations on a lattice L can be extended via e-operators only to lattices that are isomorphic to the lattice of intervals of L.
{"title":"On limitations of e-Operators","authors":"Juscelino Araújo , Benjamín Bedregal , Ana Shirley Monteiro , Regivan Santiago , Eduardo Palmeira","doi":"10.1016/j.fss.2026.109832","DOIUrl":"10.1016/j.fss.2026.109832","url":null,"abstract":"<div><div>This paper studies <em>e</em>-operators. They are a class of mappings that allow the extension of operations defined on a lattice to a larger one while preserving key algebraic properties. A characterization of these mappings is presented. It is shown that operations on a lattice <em>L</em> can be extended via <em>e</em>-operators only to lattices that are isomorphic to the lattice of intervals of <em>L</em>.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109832"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-15Epub Date: 2026-02-18DOI: 10.1016/j.fss.2026.109833
Naser Zamani
Let R be a commutative ring with identity, ξ a fuzzy ideal of R, and let M be an R-module. Let λ be a finitely generated fuzzy submodule of M such that . It is proved that there exist a ∈ ξ1 such that . Then, using this result, a proof of fuzzy version of Nakayama’s lemma is given.
{"title":"On fuzzy submodules and fuzzy Nakayama’s lemma","authors":"Naser Zamani","doi":"10.1016/j.fss.2026.109833","DOIUrl":"10.1016/j.fss.2026.109833","url":null,"abstract":"<div><div>Let <em>R</em> be a commutative ring with identity, <em>ξ</em> a fuzzy ideal of <em>R</em>, and let <em>M</em> be an <em>R</em>-module. Let <em>λ</em> be a finitely generated fuzzy submodule of <em>M</em> such that <span><math><mrow><mi>ξ</mi><mo>⊙</mo><mi>λ</mi><mo>=</mo><mi>λ</mi></mrow></math></span>. It is proved that there exist <em>a</em> ∈ <em>ξ</em><sub>1</sub> such that <span><math><mrow><msub><mn>1</mn><mrow><mi>N</mi><mo>(</mo><mn>1</mn><mo>+</mo><mi>a</mi><mo>)</mo></mrow></msub><mo>⊙</mo><mi>λ</mi><mo>=</mo><msub><mn>1</mn><mi>θ</mi></msub></mrow></math></span>. Then, using this result, a proof of fuzzy version of Nakayama’s lemma is given.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109833"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-15Epub Date: 2026-02-06DOI: 10.1016/j.fss.2026.109815
Deli Zhang , Radko Mesiar , Endre Pap
The Sugeno integral as a typical non-additive integral, is widely used in decision-making, comprehensive evaluation, and classification problems involving uncertainty or fuzziness. The concept of Sugeno integrals originated from Sugeno, and many scholars have effectively promoted its application. To this day, further development of Sugeno integrals remains a significant research direction. This paper aims to further advance the theory of Sugeno integrals by first introducing a new integral, known as the double set-function Sugeno integral (DSSI). This DSSI extends the original Sugeno integral, which was based on a single fuzzy measure, to one that is based on both set-functions and fuzzy measures. The paper also explores the monotonicity of this integral and its Jensen’s inequality, among other properties. Secondly, it discusses the convergence theorems for two types of integral sequences: those involving set-function sequences and those involving function sequences. It derives several convergence theorems, including the monotone convergence theorems, Fatou’s lemmas, and dominated convergence theorems. Finally, the paper examines discrete DSSI, provides its specific representation, and demonstrates through examples that it outperforms classical Sugeno integrals in decision-making problems.
{"title":"On double set-function Sugeno integrals","authors":"Deli Zhang , Radko Mesiar , Endre Pap","doi":"10.1016/j.fss.2026.109815","DOIUrl":"10.1016/j.fss.2026.109815","url":null,"abstract":"<div><div>The Sugeno integral as a typical non-additive integral, is widely used in decision-making, comprehensive evaluation, and classification problems involving uncertainty or fuzziness. The concept of Sugeno integrals originated from Sugeno, and many scholars have effectively promoted its application. To this day, further development of Sugeno integrals remains a significant research direction. This paper aims to further advance the theory of Sugeno integrals by first introducing a new integral, known as the double set-function Sugeno integral (DSSI). This DSSI extends the original Sugeno integral, which was based on a single fuzzy measure, to one that is based on both set-functions and fuzzy measures. The paper also explores the monotonicity of this integral and its Jensen’s inequality, among other properties. Secondly, it discusses the convergence theorems for two types of integral sequences: those involving set-function sequences and those involving function sequences. It derives several convergence theorems, including the monotone convergence theorems, Fatou’s lemmas, and dominated convergence theorems. Finally, the paper examines discrete DSSI, provides its specific representation, and demonstrates through examples that it outperforms classical Sugeno integrals in decision-making problems.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109815"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146175574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-15Epub Date: 2026-02-04DOI: 10.1016/j.fss.2026.109805
Juntao Wang , Yanhong She , Gustavo Pelaitay , William Zuluaga Botero , Mei Wang
The category , whose objects are MV•-algebras, is the image of the category , whose objects are MV-algebras, under the categorical equivalence induced by the Kalman functor K. The main aim of this paper is to lift this equivalence to the level of the category , whose objects are implicative very true MV-algebras, and the category , whose objects are implicative very true MV-algebras. Based on this, we then prove that the logic of implicative very true MV-algebras is complete and semilinear. In this paper, we first introduce the notions of implicative very true operators and their duals on MV-algebras. The resulting classes of algebras will be called MVivt-algebras and MVsvf-algebras, respectively, and we discuss the relations between MVivt-algebras and other previously introduced related structures. Subsequently, we introduce the notion of MV-algebras and show that the classes of MVivt-algebras and MV-algebras are in one-to-one correspondence. We further prove a categorical correspondence between the categories and via the functor K, which is motivated by an old construction of Kalman. Finally, we define the logic , whose Lindenbaum–Tarski algebra is an MV-algebra, and prove that it is complete and semilinear.
{"title":"Kalman structures derived from implicative very true MV-algebras","authors":"Juntao Wang , Yanhong She , Gustavo Pelaitay , William Zuluaga Botero , Mei Wang","doi":"10.1016/j.fss.2026.109805","DOIUrl":"10.1016/j.fss.2026.109805","url":null,"abstract":"<div><div>The category <span><math><msup><mi>MV</mi><mo>•</mo></msup></math></span>, whose objects are MV<sup>•</sup>-algebras, is the image of the category <span><math><mi>MV</mi></math></span>, whose objects are MV-algebras, under the categorical equivalence induced by the Kalman functor <strong>K</strong>. The main aim of this paper is to lift this equivalence to the level of the category <span><math><msub><mi>MV</mi><mrow><mi>ivt</mi></mrow></msub></math></span>, whose objects are implicative very true MV-algebras, and the category <span><math><msubsup><mi>MV</mi><msup><mrow><mi>ivt</mi></mrow><mo>•</mo></msup><mo>•</mo></msubsup></math></span>, whose objects are implicative very true MV<span><math><msubsup><mrow></mrow><msup><mrow><mi>ivt</mi></mrow><mo>•</mo></msup><mo>•</mo></msubsup></math></span>-algebras. Based on this, we then prove that the logic <span><math><msubsup><mi>Ł</mi><msup><mrow><mi>ivt</mi></mrow><mo>•</mo></msup><mo>•</mo></msubsup></math></span> of implicative very true MV<span><math><msubsup><mrow></mrow><msup><mrow><mi>ivt</mi></mrow><mo>•</mo></msup><mo>•</mo></msubsup></math></span>-algebras is complete and semilinear. In this paper, we first introduce the notions of implicative very true operators and their duals on MV-algebras. The resulting classes of algebras will be called MV<sub><em>ivt</em></sub>-algebras and MV<sub><em>svf</em></sub>-algebras, respectively, and we discuss the relations between MV<sub><em>ivt</em></sub>-algebras and other previously introduced related structures. Subsequently, we introduce the notion of MV<span><math><msubsup><mrow></mrow><mrow><mi>i</mi><mi>v</mi><msup><mi>t</mi><mo>•</mo></msup></mrow><mo>•</mo></msubsup></math></span>-algebras and show that the classes of MV<sub><em>ivt</em></sub>-algebras and MV<span><math><msubsup><mrow></mrow><mrow><mi>i</mi><mi>v</mi><msup><mi>t</mi><mo>•</mo></msup></mrow><mo>•</mo></msubsup></math></span>-algebras are in one-to-one correspondence. We further prove a categorical correspondence between the categories <span><math><msub><mi>MV</mi><mrow><mi>ivt</mi></mrow></msub></math></span> and <span><math><msubsup><mi>MV</mi><msup><mrow><mi>ivt</mi></mrow><mo>•</mo></msup><mo>•</mo></msubsup></math></span> via the functor <strong>K</strong>, which is motivated by an old construction of Kalman. Finally, we define the logic <span><math><msubsup><mi>Ł</mi><mrow><mi>i</mi><mi>v</mi><msup><mi>t</mi><mo>•</mo></msup></mrow><mo>•</mo></msubsup></math></span>, whose Lindenbaum–Tarski algebra is an MV<span><math><msubsup><mrow></mrow><mrow><mi>i</mi><mi>v</mi><msup><mi>t</mi><mo>•</mo></msup></mrow><mo>•</mo></msubsup></math></span>-algebra, and prove that it is complete and semilinear.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"533 ","pages":"Article 109805"},"PeriodicalIF":2.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146175573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-22DOI: 10.1016/j.fss.2026.109792
Lele Wang , Ruimei Zhang , Beibei Li , Ju H. Park , Mao Chen
This paper delves into the leader-follower consensus problem of Takagi-Sugeno (T-S) fuzzy multi-agent systems (MASs) subject to channel-dependent denial-of-service (DoS) attacks. Firstly, considering the asynchronous attacks on communication channels by different adversaries, a channel-dependent attack model for T-S fuzzy MASs is established, in which the topology is switched and each specific topology is regarded as a distinct attack mode. For each attack mode, a corresponding improved hybrid triggering mechanism (HTM) is newly designed. In the improved HTM, time-triggered scheme (TTS) and dynamic event-triggered scheme (DETS) are integrated, and the switching between these two schemes is governed by a Bernoulli variable at data-transmission instants. Compared with traditional triggering mechanisms, the improved HTM offers enhanced resource utilization efficiency. Besides, based on the improved HTM, a distributed attack-mode-driven hybrid-triggered (HT) control strategy is designed to mitigate the impacts of DoS attacks. Furthermore, under the designed distributed attack-mode-driven HT control protocols, theoretical results are derived to guarantee the leader-follower consensus of T-S fuzzy MASs. Finally, two simulation examples are provided to demonstrate the feasibility and effectiveness of the proposed results.
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